A square matrix in which all diagonal entries are equal and all off-diagonal entries are zero is called a scalar matrix. Or we can say that a diagonal matrix in which all the diagonal entries are equal is called a scalar matrix. We will consider some examples.
Here the diagonal entries are equal, but the off-diagonal entries are not zero. So this is now a scalar matrix.
Here the diagonal entries are 2 and the off-diagonal entries are 0, so this is a scalar matrix.